Derivative and asymptotes of f(x)=5/x²-9

[blakejohnston]

F(x)=5/(x^2)-9

Find F'(x)&F''(x)
Find the Vertical Asymptote, Horizontal, and Slant

 

[Prove It]

F(x)=5/(x^2)-9

Find F'(x)&F''(x)
Find the Vertical Asymptote, Horizontal, and Slant

Is your function $\displaystyle \begin{align*} \frac{5}{x^2} - 9 \end{align*}$ or $\displaystyle \begin{align*} \frac{5}{x^2 - 9} \end{align*}$?

 

[blakejohnston]

The second.

 

[Prove It]

Write it as $\displaystyle \begin{align*} 5 \left( x^2 - 9 \right) ^{-1} \end{align*}$ and use the Chain Rule.

 

[Nikolas7]

first derivative: -10x/(x^2-9)^2

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The second derivative: (-10(x^2-9)^2+10x(2(x^2-9)2x))/(x^2-9)^4